Tag Archives: Stephen Wolfram

I was invited to the complex systems laboratory of the Université de Montréal this week to present emergent urbanism to their twenty-member large research group. Click through to SlideShare in order to see the full text of the presentation under the “notes on” tab. The entire text is in French, however I know a significant share of this website’s visitors enjoy French once in a while.

﻿

If someone wants to sponsor me for a translation in English, email me and I’ll upload one very soon. Otherwise my hands are quite full at the moment, it might be a while before I get around to it.

Thanks to Rodolphe Gonzales from the Complex Systems Lab for the invitation. You can read about their work here.

I often wonder if it would be possible to do any kind of serious study into urban morphology without the help of Google Earth. I know it has been indispensable to my studies, perhaps as indispensable as the microscope is to biologists. Google Earth is our macroscope, it allows us to see what is too large to see with the naked eye. But no matter how useful satellite photography is, you cannot truly see depth without aerial photography, and the master of aerial photography is without a doubt French photographer Yann Arthus-Bertrand, famous for enormous coffee-table books filled with photography so rich as to be overwhelming.

Arthus-Bertrand has made the jump to high-definition cinematography and directed a “documentary” (there is really no accurate way to describe this film) called Home, which was released free of charge on the Internet a few weeks ago. You can watch it on YouTube or download it from your favorite BitTorrent source. The film is awe-inspiring. Here are some still images I extracted.

The film is a tour of Earth’s ecologies, starting from elementary life to cities. The most striking images are those of natural cities, particularly one which seems to grow out of the rock as if it were only a feature of it. And who can argue that it isn’t? But that detail seems to escape the narrative.

Yann Arthus-Bertrand’s talent is undeniable, at some point in the film he even makes Manhattan seem small. But the film quickly turns into a vessel of green propaganda (sponsored by the Gucci fashion house) while it could have been a celebration of mankind’s ties to nature. At the climax of its alarmism, the foundation of the green mindset is spelled out with as much emphasis as the narrator can apply. Denouncing the thaw of Siberian permafrost, the narrator recites “if the permafrost melts, the methane released would cause the greenhouse effect to race out of control with consequences no one can predict.” At no point in the film does the alarm in her voice sound so grave. It is not so much climate change that is feared, but the unknown, any change at all.

The obsession with control and prediction is tragically what has caused the most destruction and chaos in our human ecologies. It is control that dictates that homes may not be owned in the world’s sprawling slums, in the name of upholding a failed prediction, city planning. Because slum homes can be summarily demolished the slums remain in squalid poverty, vulnerable to any environmental change, man-made or not. The only true sustainability in a chaotic world is the ability to renew our environments for any change we meet, and control and prediction are an obstacle to this.

Green politics fails not because it relies on facts that are incorrect, but because it relies on facts that are inherently unknowable. We can sound the alarm about the total global population, the fact is we have absolutely no idea what the total global population is. We can at best obtain an estimate, but that estimate is useless for any kind of action. Action in a complex system is local and does not rely on global knowledge, but only on reacting to local conditions. The environment always tells you what to be doing in the moment.

In its obsession with control, the film ends up making recommendations for creating the same kind of technocratic utopia that was promised to us by the modernists. It praises one of the world’s poorest countries for having one of the most intensive state schooling program, evading a causal link between poverty and control of children’s minds. The ultimate solution to climate change proposed is to cover the world’s open land with solar panels, and the seas with wind farms, an act that would be as destructive to the environment as all the other monocultures denounced in the film. (And no one dares ask where those solar panels came from.)

Never is a serious look taken at the process of the natural cities, which to someone trapped in the paradigm of control and prediction would make absolutely no sense, but which Christopher Alexander masterfully demystifies in The Nature of Order. Only through such a revolution can we avoid repeating the chaos of modernism with a green twist.

People trapped in the mindset of prediction cannot think beyond simple physical processes (type I and II of Wolfram’s classification). These processes are always highly unstable and prone to die with any disruption. But life is not a simple process. It is a process that is always expanding, growing exponentially to fill any space it can fit into. Biologists quarantined a volcanic island that appeared into existence in the 1960’s near Iceland. They wanted to see how life colonized it. This process has taken place at astonishing speed, and today the island teems with life and has a rich cover of top soil, bewildering the biologists. The real threat to the island is not ecological disequilibrium, but the inevitable erosion back into the ocean.

Life is the most powerful force in the universe. It will take anything the Earth does to it. But unless we adopt life as our own social paradigm, we will not fare well. If we base our society on control instead of growth, the first unpredictable shock we witness will cause our collapse. So watch Home, be inspired by it, but do yourself a favor and turn the sound off.

The qualities of an emergent city

The adoption of mass-production processes, or development, in substitution for spontaneous urban growth in the mid-20th century created for the first time a phenomenon of alienation between the inhabitants and their environment. While the physical features of spontaneous cities could be traced to complex histories of families, businesses, and organizations, the physical features of planned cities owe their origin only to the act of planning and speculation. This has severe consequences towards the sustainability of place as there will not grow any particular attachment by the residents, their presence there being only a temporary economic necessity and not the outcome of their life’s growth. Mass-production of the environment left people as nothing more than consumers of cities where they used to be their creators. A building culture was replaced with a development industry, leaving the landscape culture-less and with no particular sense of identity. This took place despite the evidence that a building which has a unique history and has been fitted to someone’s life, as opposed to speculatively produced, generates market value for that property. (Alexander, 1975) This is why, although the demolition of so-called “slums” to replace them with modern housing projects created a great deal of opposition against urban renewal programs, the demolition of the housing projects later on did not lead to a popular preservationist opposition. They were not the physical expression of any culture.

In additional to cultural patterns, spontaneous settlements also have a peculiar morphology that has not successfully been imitated by modern growth processes. Spontaneous settlement processes give individuals full freedom to determine the boundaries of their properties. Spontaneous settlement is one where total randomness in building configuration is allowed, with no pre-determined property lines acting as artificial boundaries. Buildings and building lots as such acquire general configurations comparable to cell structure in living tissues, unique sizes and boundaries that are purely adapted to the context in which they were defined. In the absence of abstract property boundaries, property rights are bounded by real physical limits such as a neighbor’s wall. (Hakim, 2007)

Very attractive spontaneous cities have a specific pattern of the urban tissue. It consists of similar vernacular buildings that appear very simple when considered individually, but produce a visually fascinating landscape when considered as a whole. This is a form of fractal geometry. In mathematics a fractal is a geometric object of infinite scale that is defined recursively, as an equation or computation that feeds back on itself. For example the Sierpinski triangle is defined by three triangles taking the place of one triangle as in figure 4.

Figure 4. A triangle triggers a feedback function that produces three triangles, which themselves trigger the feedback function to produce nine triangles, and so on. This process can unfold as long as computational resources can be invested to increase the complexity of the object.

The Mandelbrot Set is a much more interesting fractal that is defined as a simple recursive mathematical equation, yet requires a computation to visualize in its full complexity. When computing how many cycles of feedback it takes for the equation to escape to infinity for specific coordinates, figure 5 is the outcome.

Figure 5. The image on the right is a deeper magnification of the image on the left, produced with a narrower range of coordinates as the input of the Mandelbrot set’s feedback function.

In addition to its remarkable similarity to natural phenomena, this form of geometric order informs us of a very important law in geometry: a feedback loop that is fed through the same function will produce an ordered but unpredictable geometric pattern out of any random input.

This tells us why cities of vernacular buildings have such appealing geometric properties at the large scale, despite being often shabby and improvised at the scale of individual buildings. Shanties made of scrap metal and tarp look rough at the scale of the material, but because multiple shanties share the construction process and originate from similar feedback conditions they form an ordered geometric pattern with its specific “texture”. The same process takes place at other scales of feedback, for example the production of a door. Whether the input for one door is larger, taller, wider than another door, if the same production process is employed the two doors will contribute to the overall fractal order of the urban space. This law has been employed not only in traditional and spontaneous cities, but also for modern urban planning initiatives. In the New York City neighborhood of Times Square the structure of billboard advertisements is defined by a building code that determines their configuration in relation to the configuration of the building. The outcome is a unique tissue of advertisement billboards that has become more characteristic of the neighborhood than the buildings themselves, which are not produced by a shared feedback function.

Fundamentals of urban complexity

Christopher Alexander showed in A City is not a Tree (Alexander, 1965) that social and economic networks formed complex semi-lattice patterns, but that people who observed them limited their descriptions to a simple mathematical tree of segregated parts and sub-parts, eliminating connections in the process. (Figure 6 compares the structure of a tree and semi-lattice.) In attempting to plan for urban structure, a single human mind, without a supporting computational process, falls back on tree structures to maintain conceptual control of the plan, thus computing below spontaneous urban complexity, a phenomenon that is consistent with Wolfram’s theory of computational irreducibility of complex systems. (Computational irreducibility states that the only accurate description of a complex system is the system itself and that no abstraction or reduction to a simpler process is possible.) Nikos A. Salingaros later detailed the laws of urban networks in Theory of the Urban Web. (Salingaros, 1998) Network connections form between nodes that are complementary, and therefore the complexity of networks depends on an increasing diversity of nodes. Salingaros describes the urban web as a system that is perpetually moving and growing, and in order to do this the urban tissue has to grow and move with it. Consider for example the smallest social network, the family. Debate over accessory units or “granny flats” has intensified as normal aging has forced the elderly out of their neighborhoods and into retirement complexes, while at the other end of the network young adults entering higher education or the labor market vanish from a subdivision, leaving a large homogeneous group of empty-nesters occupying what was once an area full of children, and often forcing school closures (a clear expression of unsustainability).

Figure 6. A comparison of a tree pattern on the left and a semi-lattice pattern on the right. The tree structure is made of groups and sub-groups that can be manipulated separately from others. The semi-lattice pattern is purely random without distinct sub-parts.

These social networks grow more complex with increasing building density, but a forced increased in density does not force social networks to grow more complex. For instance the spontaneous settlements of slums in the developing world show remarkable resilience that authorities have had difficulty acknowledging. Because of squalid living conditions authorities have conducted campaigns to trade property in the slum for modern apartments with adequate sanitary conditions. To the authorities’ befuddlement some of the residents later returned to live in the slum in order to once again enjoy the rich social networks that had not factored in the design of the modern apartments and neighborhoods, demonstrating that the modern neighborhoods were less socially sustainable than the slums.

In commercial networks, space syntax research (Hillier, 1996), using a method for ranking nodes of semi-lattice networks, has shown that shops spontaneously organize around the multiple scales of centrality of the urban grid at its whole, creating not only commercial centers but a hierarchy of commercial centers that starts with sporadic local shops along neighborhood centers and goes all the way to a central business district located in the global center of the spatial network. The distribution of shops is therefore a probabilistic function of centrality in the urban grid. Because the information necessary to know one’s place in the hierarchy of large urban grids exceeds what is available at the design stage, and because any act of extension or transformation of the grid changes the optimal paths between any two random points of the city, it is only possible to create a distribution of use through a feedback process that begins with the grid’s real traffic and unfolds in time.

The built equilibrium

Although they may appear to be random, new buildings and developments do not arise randomly. They are programmed when the individuals who inhabit a particular place determine that the current building set no longer provides an acceptable solution to environmental conditions, some resulting from external events but some being the outcome of the process of urban growth itself. It is these contextual conditions that fluctuate randomly and throw the equilibrium of the building set out of balance. In order to restore this equilibrium there will be movement of the urban tissue by the addition or subtraction of a building or other structure. In this way an urban tissue is a system that fluctuates chaotically, but it does so in response to random events in order to restore its equilibrium.

This explains why spontaneous cities achieve a natural, “organic” morphology that art historians have had so much difficulty to describe. Every step in the movement of a spontaneous city is a local adaptation in space and time that is proportional to the length of the feedback loops and the scale of the disequilibrium. For spontaneous cities in societies that experience little change the feedback loops are short and the scale of disequilibrium small, and so the urban tissue will grow by adding sometimes as little as one room at a time to a building. Societies experiencing rapid change will produce very large additions to the urban tissue. For example, the skyscraper index correlates the construction of very tall buildings with economic boom-times, and their completion with economic busts. The physical presence of a skyscraper is thus the representation of a major disequilibrium that had to be resolved. (Thornton, 2005) The morphology of this change is fractal in a similar way that the movement of a stock market is, a pattern that Mandelbrot has studied. In general we can describe the property of a city to adapt to change as a form of time-complexity, where the problems to be solved by the system at one point in time are different from those to be solved at a later point in time. The shorter the time-span between urban tissue transformations, meaning the shorter the feedback loops of urban growth, the closer to equilibrium the urban tissue will be at any particular point in time.

Modern urban plans do not include a dimension of time, and so cannot enable the creation of new networks either internally or externally. They determine an end-state whose objective is to restore a built equilibrium through a large, often highly speculative single effort. They accomplish this by creating a large-scale node on existing networks. In order for such a plan to be attempted the state of disequilibrium in the built environment must have grown large enough to justify the immense expense of the new plan. This is why development will concentrate very large numbers of the same building program in one place, whether it is a cluster of 1000 identical single-family homes or a regional shopping mall, just like the skyscraper concentrates multiple identical floors in one place. Demand for these buildings has become so urgent that they can find a buyer despite the absence of local networks, the standardized building plan, or the monotonous setting. This is not as problematic for large cities for which a single subdivision is only a small share of the total urban fabric, but for smaller towns the same project can double the size of the urban fabric and overshoot the built equilibrium into an opposite and severe disequilibrium.

The mixed-used real estate development has attempted to recreate the sustainable features of the spontaneous city by imitating the morphology of sustainable local economic networks. It has not reintroduced the time dimension in economic network growth. Often this has resulted in a commercial sector that serves not the local neighborhood but the larger region first, consistent with the commercial sector being a product of large-scale economic network disequilibrium. In other developments the commercial sectors have struggled and been kept alive through subsidies from residential development, which is evidence of its unsustainability as part of the system.

This is part I of a series of excerpts of an article to be published in the International Journal of Architectural Research entitled The Principles of Emergent Urbanism. Additional parts will be posted on this blog with the editor’s permission until the complete article appears exclusively in the journal’s upcoming issue.

Of the different domains of design urban design is an oddity. While the design of a machine can be traced to a definite, deliberate act of invention, and even the design of buildings (architecture) is rooted in known production processes, the design of cities was never seriously attempted until well after cities had become a normal, ordinary aspect of civilized living, and while the design of machines and buildings was a conscious effort to solve a particular problem or set of problems, cities appeared in the landscape spontaneously and without conscious effort. This places the efficacy of urban design in doubt. The designers of machines and buildings know fully how the processes that realize their design operate, and this knowledge allows them to predictably conceive the form they are designing. Urban designers do not enjoy such a certainty.

How is it possible for what is obviously a human artifact to arise as if by an act of nature? The theory of a spontaneous order provides an explanation. According to Friedrich A. von Hayek (Hayek, 1973) a spontaneous order arises when multiple actors spontaneously adopt a set of actions that provides them with a competitive advantage, and this behavior creates a pattern that is self-sustaining, attracting more actors and growing the pattern. This takes place without any of the actors being conscious of the creation of this pattern at an individual level. The spontaneous order is a by-product of individuals acting in pursuit of some other end.

In this way cities appear as agglomerations of individually initiated buildings along natural paths of movement, which originally do not require any act of production as dirt paths suffice. As the construction of individual buildings continues the most intensely used natural paths of movement acquire an importance that makes them unbuildable and these paths eventually form the familiar “organic” pattern of streets seen in medieval cities. This process still takes place today in areas where government is weak or dysfunctional, notably in Africa where urban planning often consists of catching up to spontaneous settlement, and in the infamous squatter slums that have proliferated in the 20th century.

A transect of the city of Tultepec in Mexico provides a snapshot of the different phases of spontaneous urban growth. (Google Earth image)

As urbanization becomes denser, the increasing proximity of concurrent, competing individual interests causes conflicts between the inhabitants of the emerging town. Individuals build out their properties in such a way that it interferes with others, for example by blocking paths or views. These acts threaten the sustainability of the spontaneous order, and to resolve this situation the parties involved appeal to the same judges that rule on matters of justice. These judges, again according to Hayek, are required to restore and preserve the spontaneous order with their rulings. These rulings provide the first building regulations and, when government authority becomes powerful enough to do so, are compiled into comprehensive building codes to be applied wherever the force of that government extends. (Hakim, 2001)

The compiled building codes are later brought by colonists to create new settlements, reproducing the morphology across multiple towns but each time in a pattern that is adapted to the local context. Early town planning efforts are attempts at regularizing the building codes in order to plan for long-term organization of cities, but maintain the spontaneous production process. Most notably the rapid urbanization of New York City was accomplished by very simple rules on the size of blocks laid out in the 1811 Commissioners Plan for New York. Unlike the experience of urbanization in previous centuries, where urban growth was slow and often stagnant, the urbanization of New York took place in a time of rapid social and economic changes, and the city government had to invent building codes involving issues that never could arise in a pre-capitalist society: first the tenement, then the skyscraper, and ultimately, the automobile.

Modernism: the replacement for the spontaneous order

Architects and urban planners of the early 20th century, confident in the techniques of engineering and industrial production, believed that the spontaneous city had become irrational and had to be replaced with a new design fully integrating new industrial technology. The Swiss architect Le Corbusier is famous for designing a complete city around the automobile and building models of his design. In so doing he adopted a process of urbanization that was completely planned hierarchically, applying the processes familiar to architects at the scale of an entire city. He also ridiculed the morphology of spontaneous cities as being the product of donkey-paths.

This scale model of Le Corbusier’s Plan Voisin marks the turning point where city plans as constraints on individual initiative are replaced with architectural design at the scale of millions of inhabitants. (Le Corbusier, 1964)

Although the architectural program of high-rise living of Le Corbusier was discovered to be a colossal failure, the modernist process of development replaced spontaneous urbanization in the industrialized world. The housing subdivision substituted adequately for the high-rise tower block, providing affordable housing in large numbers to a war-impoverished society. This production process is still in force today, separating cities into three distinct zones: residential subdivisions, industrial and office parks, and commercial strips.

Modern city planning has been successful at its stated objective, producing a city designed specifically around automobile use, yet it was immediately and has been perpetually the target of criticisms. Most significantly the vocabulary of these criticisms had to be invented in order to spell out the critics’ thoughts because the type of deficiency they were observing had never been seen. Words like placeless or cookie-cutter were invoked but fell on the deaf ears of urban planners who were trained in Cartesian processes and industrial production techniques.

The most devastating criticism of modernist urban planning came in the form of a sociological study and personal defense of the spontaneous city, the book Death and Life of Great American Cities by Jane Jacobs. (Jacobs, 1961) In it she described in great details how the functions of a spontaneous city related and supported each other. Her concluding chapter, the kind of problem a city is, is still the most relevant. In it she attacks the scientific foundations of urban planning at a paradigmatic level, and claims that the methodology of the life sciences, at the time undergoing the revolution created by the discovery of DNA, is the correct approach to studying cities.

Death and Life of Great American Cities has been adopted by contemporary urban planners as a textbook for urbanity. Its descriptions of the characteristics of a city are now the models upon which new developments are planned. The old urban development of housing subdivisions and office parks is being substituted for the new urban development that has streets, blocks, and mixed uses, just as Jacobs had described to be characteristic of life in the city. A major difference between Jane Jacobs’ preferred city and the new urban plans remains. The layout of mixed uses is organized and planned in the same process as Le Corbusier planned his city designs. The scientific suggestions of Jacobs have been ignored.

The discovery of emergence and complexity science

In the time since Jacobs published her attack on planning science molecular biology has made great technological achievements and provided countless insights into the morphology of life. In parallel the computer revolution has transformed the technology of every human activity, including that of design. But the computer revolution brought along some paradigm-altering discoveries along with its powerful technology. In geometry, the sudden abundance of computing power made it possible for Benoit Mandelbrot to investigate recursive functions and his discovery, fractal geometry, generated a universe of patterns that occurred in many aspects of the physical universe as well as living organisms. (Mandelbrot, 1986)

Some thinkers saw that the life sciences were part of a much more general scientific domain. They formed the Santa Fe Institute and under the label complexity studied not only organisms but also groups of organisms, weather systems, abstract computational systems and social systems. This research formed a body of theory called complexity science that has resulted in the creation of similar research institutes in many other places, including some centers dedicated specifically to urban complexity.

Their scientific revolution culminated in two major treatises within the last decade, both from physicists practicing in a field of complexity. The first was A New Kind of Science by computer scientist and mathematician Stephen Wolfram (Wolfram, 2002), where he presents an alternative scientific method necessary to explore the type of processes that traditional science has failed to explain, presenting a theory of the universe as a computational rule system instead of a mathematical system. The second was The Nature of Order (Alexander, 2004) by architect Christopher Alexander, where he presents a theory of morphogenesis for both natural physical phenomena and human productions.

A definition of emergence

To define what is meant by emergence we will use the abstract computational system upon which Wolfram bases his theories, the cellular automaton. Each cell in a row is an actor, making a decision on its next action based on its state and the states of its direct neighbors (its context). All cells share the same rule set to determine how to do this, that is to say all cells will act the same way with the same context. In this way each row is the product of the actions of the cells in a previous row, forming a feedback loop. The patterns of these rows are not in themselves interesting, but when collected in a sequence and displayed as a two-dimensional matrix, they develop complex structures in this dimension.

The 30th rule of all possible rules of one-dimensional cellular automata produces a chaotic fractal when displayed as a two-dimensional matrix, but most other rules do not create complex two-dimensional structures. The first line of the matrix is a single cell that multiplies into three cells in the second line in accordance with the transformation rules pictured below the matrix. This process is reiterated for the change from the second to the third line, and so on. All the information necessary to create structures of this complexity is contained within the rules and the matrix-generating process. (Wolfram, 2002)

The same general principle underlies all other emergent processes. In a biological organism a single cell multiplies into exponentially greater number of cells that share the same DNA rules. These cells create structures in a higher dimension, tissues and organs, which form the entire organism. In the insect world complex nests such as termite colonies emerge from the instinctual behavior of individual termites. And in urbanization, buildings form into shopping streets, industrial quarters and residential neighborhoods, themselves overlapping into a single whole system, the city.

Until very recent times, a study entitled Julian of Ascalon’s Treatise of Design and Construction Rules From Sixth-Century Palestine might have been categorized somewhere in-between ancient history and archeology of architecture, if not relegated to the dusty shelves of legal scholarship. Although it deals with one of the most sought-after secrets of architecture, how to build the charming Mediterranean towns of Greece, Spain, North Africa, the Near East and many other places, this is not immediately obvious from the content of the treatise. The reason for this is that the treatise does not so much describe the form of the town as the process for building it, and the process turns out to be emergent. Unless the reader makes the link from process to form, the rules described will make no more sense than the rules for a cellular automaton out of context.

It is tragic that enormous amounts of resources have been spent attempting to recreate the Mediterranean town with no clue as to the underlying source of its complexity. Montreal itself has the world famous Habitat 67, a confusing pastiche of the memories that architect Moshe Safdie brought back from his land of birth, which he had in common with Julian of Ascalon. Habitat 67 was intended to be a low-cost solution to housing, but it never was taken seriously as a model for urban habitat, and its current untrendiness spares it from being labeled fake complexity. That an attempt to emulate the architecture of some of the poorest people of previous centuries would result in an expensive failure testifies to the inadequacy of modern production processes, but also of the wealth inherent in those simple traditional production processes. The beauty resulting from large aggregations of simple buildings has turned many towns into tourist destinations. There is value in process.

The complexity demonstrated by the constructions of pre-modern civilizations may be a direct consequence of their material poverty. Most people will claim that the loss of building quality is a result of culture, and so we must change our own culture through education. That is not a complete answer. Cultures are stored in information technologies and media. The modern era coincides with the invention of printing, making it possible for the first time to reproduce information in large quantities at low costs. As information technologies have progressed and become more affordable, building processes have become increasingly dependent on large amounts of descriptive information, with blueprints describing in every minute detail how to compose a building. And now that CAD software can describe and store nearly limitless information, whole new forms of buildings have become possible.

All of this progress has only enabled builders to become lazier with information. Pre-modern builders, limited to oral communication and their brains to hold information, had to employ very sophisticated means of information compression to communicate and simply remember their cultures. This lead them to rely on simple processes the likes of which are behind the complexity in fractal geometry and cellular automata to build their environments – very short sequences of information that can be utilized to generate fully complex forms. Christopher Alexander even used as an example, in The Nature of Order, the production of a boat that had been coded into a song that the builders recited while creating the boat, adding a mnemotechnical aspect to the storage of cultural information that was essential to pre-modern survival.

Without knowing how traditional cultures were stored, we had no idea how to inspire ourselves from them. Modern and post-modern architects attempted in vain to imitate traditional building using their own, lazy information technologies, and succeeded only in building pastiche of complexity. The breakthroughs in complexity theory of the past decades finally gave us the opportunity to decode the mysteries of historic building cultures by showing us what kind of information to search for. What was right in front our noses suddenly becomes deeply meaningful.

It is to his great credit that Besim S. Hakim went looking specifically for the source of the emergent forms of Mediterranean towns in treatises of building laws. From his study of the treatise of Julian of Ascalon, but also of those of Muslim scholars around the Mediterranean, he was able to identify the underlying process that generates the complex morphology all towns of the region have in common, and that so many have sought to imitate. It is no exaggeration to call this pioneering work in complexity.

The space of Hakim’s search began in the Islamic world, with the treatise of Ibn al-Rami from Tunis in circa 1350. Tracing the origins of the practices described in the treatise, references to treatises written in Egypt, Arabia, Tunisia and Andalusia in previous centuries were researched until the treatise of Julian of Ascalon was uncovered. Written in Palestine to describe the local building customs in order to provide the Byzantine empire with an improved legal system, this particular treatise’s value is its longevity. After propagating throughout Greek civilization as part of a general book of laws (the Hexabiblos), its authority was invoked in decisions dating as recently as the 19th century. Hakim infers the origins of these shared practices, and the shared morphology of regions as far apart culturally, linguistically and geographically, as Andalusia, Greece and Palestine, to customs from ancient Babylonian civilization that had spread to the Eastern Roman Empire.

The goal shared by these treatises is a definition of urbanism as relevant today as it was in Babylon:

The goal is to deal with change in the built environment by ensuring that minimum damage occurs to preexisting structures and their owners, through stipulating fairness in the distribution of rights and responsibilities among various parties, particularly those who are proximate to each other. This ultimately will ensure the equitable equilibrium of the built environment during the process of change and growth. (Hakim, Mediterranean urban and building codes: origins, content, impact, and lessons, p. 24)

Here we see what the underlying error of Habitat 67 was. It was designed as a single static building imitating a process that made a living tissue out of many individual acts of simple building. The codes of the Mediterranean treat the town as a living, whole structure in movement that must be preserved while it achieves equilibrium with a changing environment and society.

Perhaps the most relevant conclusion of this research is the identification of proscriptive and prescriptive rules for building.

Proscription is an imposed restraint synonymous with prohibition as in ‘Thou shalt not’, for example, you are free to design and manipulate your property provided you do not create damage on adjacent properties. Prescription is laying down of authoritative directions as in ‘Thou shalt’, for example, you shall setback from your front boundary by (x) meters, and from your side boundaries by (y) meters regardless of site conditions. Byzantine codes in many instances included specific numeric prescriptions, unlike their Islamic counterparts that tended not to include them. (Hakim, Mediterranean urban and building codes: origins, content, impact, and lessons, p. 26)

A prescription would be a rule that defines in detail what to do in a given situation. A proscription is a template for defining prescriptive rules, a pattern for a rule. Muslim scholars provided mainly proscriptions, but Julian of Ascalon’s treatise was highly prescriptive. Julian was describing in details the local building codes with the idea that they would be used to devise proscriptive rules for the empire. By accident these prescriptive rules became law and remained in force for centuries until their inability to deal with society or physical conditions radically different from sixth century Palestine made them obsolete. Although it means the codes failed to deal with changing circumstances, this gives us the chance to bridge the gap between the physical structure of built towns and the rules that generate them.

The concept of proscriptive rules also helps explain why so many different cultures with specific structural typologies can generate such similar morphology. Hakim uses as an example the problem of views. The Greeks were preoccupied with views of the sea, and their prescriptive rules obliged the preservation of view corridors in new constructions. Muslims, on the other hand, were preoccupied with the preservation of privacy and the prevention of intrusive views from one property to another. This would have very different results structurally, however those two prescriptive rules are based on the same underlying proscription. Local customs and culture could therefore be translated into prescriptive rules using the proscriptions inscribed in building treatises and the emergent morphology of those proscriptions would be symmetric from one culture to the next, while being fully adapted to local conditions.

Another significant fact that strikes out from these treatises is the importance of relationships between neighbors. The Julian of Ascalon treatise describes how to literally embed houses into each other, ultimately making them one continuous, somewhat random building created through iterated steps. But most importantly by proscribing rules as relevant to a neighborhood, Mediterranean urbanism avoids the problem of the absolutist, dare I say “Cartesian” rules of modern planning that are relative to the precisely subdivided lot the building is on. Hakim shows the wastefulness of latter rules in a comparison of the old town of Muharraq in Bahrain with a new subdivision from modern Muharraq.

The town on the left was generated using proscriptions based on neighbors, while the subdivision on the right used absolute rules planned with the subdivision. Notice that the configurations on the right waste much of the space in order to achieve a strictly Cartesian, grid-like morphology that no doubt looks orderly to the planners.

The last item of significance, and perhaps the most revolutionary, is how the proscriptions extracted by Hakim are similar in nature to the rules that Stephen Wolfram described to generate emergent complexity with cellular automata. He himself follows a proscription/prescription system, where the proscription is for example the 2 color, one-dimension elementary cellular automaton that made him famous, for which there exist 256 different prescriptive rules of neighborhood, some of which grow in time to make two-dimensional chaotic fractals. Some urban complexity researchers such as Michael Batty have been playing with cellular automata trying to reproduce urban form, but their efforts have taken them on the wrong track. The codes of historic towns behave in the same manner as a cellular automaton. This should be the focus of their research.

Whatever the potential for research, the proscriptions discovered by Besim S. Hakim are still relevant today and can be used to create the prescriptions that we need to implement an emergent urbanism relevant to the problems of today, that is to say the creation of a sustainable city and living urban tissue out of the vast urban fabric of suburban sprawl. Hakim has so far focused his work on the regeneration of historic neighborhoods by restoring the generative codes that produced them, but there is a vast potential to expand his work to non-historic neighborhoods that are in dire need of new life.

Addendum

Four regions, four cultures, one shared process generating a symmetric morphology

The immensely productive Physicist-Mathematician-Entrepreneur Stephen Wolfram theorized, based on his studies of cellular automatons in the 1980’s, that there exists four classes of physical processes in the universe. Class I is simple continuous behavior (line). Class II is repetitive behavior (checkerboard). Class III is nested, hierarchical-fractal behavior (basic fractals like the Sierpinski triangle). Class IV, the most fascinating, is chaotic behavior (random fractals such as the Mandelbrot Set). Wolfram believes that Class IV behavior, exemplified by the Rule 30 automaton, is behind the complexity we see in the universe, and that very simple generative rules produce it.

The way we as humans are used to doing engineering and to building things, we tend to operate under the constraint that we have to foresee what the things we’re building are going to do. And that means that we’ve ended up being forced to use only a very special set of programs–from a very special corner of the computational universe–that happen always to have simple foreseeable behavior. But the point is that nature is presumably under no such constraint. So that means that there’s nothing wrong with it using something like rule 30–and that way inevitably producing all sorts of complexity.

Wolfram gave this speech on his new science to big shot architecture schools at Yale, Princeton and MIT. He believes that his new science has profound implications for the generation of form in architecture. I agree with him, but not for the reasons he provided. In fact his classification of the geometric properties of different physical phenomenons provides extremely profound insight into the history of architecture, and its future.

A visit to London was what really made me appreciate this insight. London, as an architectural artifact, is quite unique in that its greatest period of growth, the period 1750-1850, coincides with the beginning of modernism in architecture, a time when architecture became in a sense aware of itself and in search of its meaning. Neoclassicism was followed by Gothic Revival, Romanesque Revival, Neo-Venetian, all of it got mixed up in eclecticism, and the invention of new materials and building processes came to confuse things even more. Regardless of stylistic debates, what may be most important about that period is that, for the first time in history, large capital funds for speculative real estate development became available. Where architecture had once been a piecemeal business occurring quite randomly, in London, for the first time ever, housing subdivisions were possible. The result was the terrace housing.

The big housing developments in London were initiated by aristocratic landowners who hired architects to plan and control the form their estates would take. Walking through Chelsea and South Kensington, one is faced with sometimes overwhelming repetition of identical houses. Class II behavior, that Wolfram claims is fundamental to engineering, is obviously visible. The architects of the estates, not really knowing the specific constraints of the future residents of the place, opted for endless repetitions of the same building. The fact that each building is a copy of the next, inadapted to the particular wants of its occupants, makes it standard behavior, far from complex.

The human mind is by nature fractal and is repulsed by Class II geometry, which is why traditionally architects have built Class III, hierarchical fractal geometry. This was employed by some terrace builders, such as the architect of the Regent’s Park estate, John Nash. Here the monotony of the model is interrupted by nesting houses in flourishes like arches, or bigger houses with large porticoes.

Classical architectural education, based on the teaching of the classical orders, trained architects in the art of doing such hierarchical decompositions of their buildings. As such most of the high western classical architecture, starting from the renaissance architecture of Alberti (the first modern architect in the sense that his name is more important than any of his buildings, not true of the medieval architects of cathedrals), is rigidly symmetrical. Classically-trained architects only expanded the scales of decomposition as the size of buildings increased, up to the neoclassical skyscrapers that modernists considered to be ridiculous. The classicals were right about the need to create fractal geometry by decomposition of what were rigid engineering plans, what the modernists claimed was ornamental crime, philosophically dishonest and replaced with elementary repetition in their designs (regression to type II geometry). People have hated architects ever since.

Whenever I read through architectural history books, even those of honest traditionalists like David Watkin, I am struck by what is clearly missing from the record. That is to say the towns built up over centuries, the accretion of simple building acts into complex symmetries. The topic is touched by some thinkers of urban morphology, typically under the label of “organic” growth, such as in The City Shaped by Spiro Kostof, but everyone appears dumbfounded by the means through which such symmetry was accomplished. And largely the whole career of Christopher Alexander has been dedicated to decoding this mystery.

But even in the 19th century, when large-scale development was sweeping London, some complex geometry was achieved. These are four distinct buildings on Lincoln’s Inn Fields.

We immediately notice that each building is different from the other, having been built for a unique purpose and therefore being a unique solution to a unique problem. Despite that, the buildings form a harmonious geometric composition because they share many transformations to which randomness is applied. Even within one building, Lincoln’s Inn on the left, randomness is visible. The tower is unique, but symmetric with the rest through shared transformations. What we are seeing here is, I believe, a genuine Class IV pattern.

How could this be possible? If Wolfram’s theory on the origins of complexity is correct, then there must be a very simple rule to produce this kind of street scape. This rule can be applied to any random architectural demand and provide a perfectly appropriate solution to an individual problem while remaining completely harmonious with other such random solutions in its neighborhood! Since such organic complexity appears in all human civilizations, then we must conclude that every single building culture in the world has known, at some point, such a rule, and has applied it to solve building problems of all forms. Without understanding how these rules created complexity, they simply repeated them after each successful building.

What to do with new technology? New technology necessarily creates a new scale into the rule, but the remaining rules are still valid. This is visible in the glass structure appended to the Royal Opera House.

We can see many shared patterns between the central structure and rightward structure, but not with the new addition on the left. Typical of modernist architecture, the left building is only made of elementary geometry, barely even qualifying it as a Class II structure. It doesn’t feel as though it belongs there at all. There is an important lesson here, one that architects I fear do not want to learn.

Wolfram claims that complexity science is about finding simple rules that can generate complexity. We can decode simple rules from traditional architecture that, even with the modest means of poor villagers, will generate complexity when applied repeatedly to random events, creating random fractals while simultaneously solving a vast diversity of unique problems. This is exactly the kind of work that good urbanists should be doing today, and from there we could allow maximum diversity in our cities without breaking symmetry and harmony at costs as low as the meanest buildings currently cost. If Wolfram is correct, then the rules may be so simple that they may be easily codified into building regulation even by the dullest bureaucrats. Then again the behavior may be so complex (that is to say there is emergence) that no a posteriori codification is even impossible, and the processes by which cities are governed may have to be completely reconsidered. Either way this is not good news for architects. If architecture is so easy, then their idiosyncratic designs are not necessary nor valuable. The big shot schools of architecture that Wolfram visited will be made irrelevant by Wolfram.
References: